Solve for $x$ and $y$ using elimination. ${5x-2y = 7}$ ${-4x-5y = -65}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $-2$ ${25x-10y = 35}$ $8x+10y = 130$ Add the top and bottom equations together. $33x = 165$ $\dfrac{33x}{{33}} = \dfrac{165}{{33}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {5x-2y = 7}\thinspace$ to find $y$ ${5}{(5)}{ - 2y = 7}$ $25-2y = 7$ $25{-25} - 2y = 7{-25}$ $-2y = -18$ $\dfrac{-2y}{{-2}} = \dfrac{-18}{{-2}}$ ${y = 9}$ You can also plug ${x = 5}$ into $\thinspace {-4x-5y = -65}\thinspace$ and get the same answer for $y$ : ${-4}{(5)}{ - 5y = -65}$ ${y = 9}$